Calculate prism and cylinder volumes from cross-sectional area and length.
Calculator route: NC/C selected to purpose; label each question
Stretch and deep challenge are optional routes for learners ready to move on. Complete the independent check before using revealed answers.
Connect & Check
Explain the method: A prism has a constant cross-section. Volume is cross-sectional area multiplied by length.
Discuss this with a partner before using the worked example.
Share
Compare starting methods
With a partner, predict the first step for: A triangular prism has cross-section base 6 cm and height 4 cm, with length 10 cm. Find its volume. Compare your reasons before viewing the model.
Present
A triangular prism has cross-section base 6 cm and height 4 cm, with length 10 cm. Find its volume.
Reveal a worked check after attempting
Triangle area = 12 cm², so volume = 120 cm³.
Apply
A cylinder has radius 3 cm and height 8 cm. Give its volume exactly.
Reveal a worked check after attempting
V = π × 3² × 8 = 72π cm³.
Apply and extend
A prism has volume 210 cm³ and cross-section area 15 cm². Find its length.
Reveal a worked check after attempting
210 ÷ 15 = 14 cm.
Optional stretch
A prism has a trapezium cross-section with parallel sides 4 cm and 8 cm and height 3 cm. Its length is 11 cm. Find the volume.
Reveal a worked check after attempting
Cross-section = (4+8)×3/2=18 cm²; volume=198 cm³.
Optional deep challenge
A cylinder and a triangular prism both have cross-sectional area 24 cm² and length 7 cm. Compare their volumes and explain.
Reveal a worked check after attempting
Both volumes are 24×7=168 cm³; the cross-section shape does not change the prism rule.
Recall & Review
Without notes, solve the Apply question again and justify one check.
Reveal a worked check after attempting
V = π × 3² × 8 = 72π cm³.
Recall & Review and prepare
Surface area and volume
Write one question about today's work to bring to the next lesson.
Save a copy of your answers before leaving this page. A revealed answer is a check, not evidence of independent mastery.
Recall & Review: feedback and extension integration
Lesson L035: Prisms and cylinders
Objective: Calculate prism and cylinder volumes from cross-sectional area and length.
I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.
Even Better If (EBI)
I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.
Stretch and deep challenge
Stretch: A prism has a trapezium cross-section with parallel sides 4 cm and 8 cm and height 3 cm. Its length is 11 cm. Find the volume.
Deep challenge: A cylinder and a triangular prism both have cross-sectional area 24 cm² and length 7 cm. Compare their volumes and explain.
